Invoker is known as one of the most complex characters in the game with his vast collection of spells, and mixing system, but he's really not that difficult in play. It is however important you have your keys set up so abilities 4 and 5 are easy to access. At levels 2-6 you will only have access to one spell, so it's important you plan which one you need before an engagement. At level 7 you can have 2 spells so you should plan effective combos. Cold Snap is good for ganks, but having Ghost Walk ready is good in case things go wrong or to further slow escaping enemies. EMP is great for teamfights as enemies might rush into battle only to find they have less mana and cannot fight back as well. A tornado will help hold them in place while the EMP builds up, and help teammates position themselves. Once you get Exort Deafening Blast works as a good AOE stun that groups enemies making it easy to drop a Meteor on them. The Quas Wex skill build I focus on in this guide however does not emphasize Exort enough for this to hit very hard until very late game (though with high Quas and Wex Deafening Blast is still an effective skill on it's own)
Starting with Blades of Attack will make last hits easier and can be built into Phase Boots which are great for positioning, and chasing. Quas at level 1 will give you great HP regeneration making you very self sufficient, and at level 2 you can get Cold Snap which is very effective for ganks making you a good choice for mid lane. Unlike most mids, your Quas HP regeneration will make you less bottle dependent than most mids. You may still wish to purchase a bottle to deny the enemy team runes/bottle and enhance your ganks.
This is when team fights become far more important, and for Invoker positioning is everything. Get those phase boots ASAP. For the actual fight EMP + Tornado provides great initiation. For more positioning power get a Force Staff or Blink Dagger (I prefer Force Staff since it gives INT and can be used to escape). Eul's provides more movement, good stats, and another disable ability for once you have used your two spells, however if your farm is doing really good you may consider skipping right to the Scythe of Vyse as it gives better stats and a better disable. Regardless of which one you choose get a Void Stone ASAP as it's a component in both and you will likely be needing the additional MP. Consider putting a single point into Exort here as it will open up a lot more spells to you, and give you additional mana regeneration on command. If your teammates have lots of good initiation abilities, you may want to just put put all your points into Exort at this point, as the spells it unlocks tend to be the harder hitting type.
Aghanim's Scepter reduces Invoke's mana cost to 0, and the cooldown can be reduced to 2 seconds. Being comfortable with combing QWE into spells really pays off here as you can replace spells on cooldowns quickly, and ensure you have the right spell for every situation. Being skilled here really pays off big time, but for your first or second game as Invoker you might not be quick enough to really take advantage of this.